Diaboloidal mirrors: algebraic solution and surface shape approximations. (2nd June 2021)

• Record Type: Journal Article
• Authors: Yashchuk, Valeriy V.; Goldberg, Kenneth A.; Lacey, Ian; McKinney, Wayne R.; Sanchez del Rio, Manuel; Padmore, Howard A.
• Is Part Of: Journal of synchrotron radiation. Volume 28:Part 4(2021)
• Page Start: 1031
• Page End: 1040
• Publication Date: 2021-06-02
• Subjects: X‐ray optics -- diaboloidal mirror -- analytical solution -- shape approximation; Synchrotron radiation -- Periodicals; Free electron lasers -- Periodicals; 539.73505
• DOI: 10.1107/S1600577521004860
• Languages: English
• ISSNs: 0909-0495

Abstract

Abstract : The diaboloidal mirror is a reflecting surface that converts a spherical wave to a cylindrical wave (or vice versa). Application of the mirror in a collimated two‐crystal monochromator will be the main application area and will allow brightness preserving focusing, even with the very small source size of a multi‐bend achromat ultra‐high‐brightness synchrotron source. An exact analytical solution for the surface shape of a diaboloidal mirror as a function of the conjugate parameters of the mirror placed in a beamline is presented. Abstract : A new type of optical element that can focus a cylindrical wave to a point focus (or vice versa) is analytically described. Such waves are, for example, produced in a beamline where light is collimated in one direction and then doubly focused by a single optic. A classical example in X‐ray optics is the collimated two‐crystal monochromator, with toroidal mirror refocusing. The element here replaces the toroid, and in such a system provides completely aberration free, point‐to‐point imaging of rays from the on‐axis source point. We present an analytic solution for the mirror shape in its laboratory coordinate system with zero slope at the centre, and approximate solutions, based on bending an oblique circular cone and a bent right circular cylinder, that may facilitate fabrication and metrology.